A B737 FLT CREW INADVERTENTLY CROSS THE HOLD SHORT LINE OF RWY 24L AT CLE RESULTING IN AN ABORTED TKOF.

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AFTER AN UNEVENTFUL LNDG ON RWY 24R AT CLE; WE RECEIVED THE FOLLOWING CLRNC; 'FLT NUMBER; CLRED ACROSS RWY 24C AND HOLD SHORT RWY 24L AT TXWY K.' AS I PROCEEDED TO CLR RWY 24C; TWR ASKED ME IF I WAS HOLDING SHORT OF RWY 24L. I IMMEDIATELY STOPPED THE ACFT. MY FIRST THOUGHT WAS; 'WHY IS HE ASKING ME THIS? I HAVEN'T EVEN CLRED RWY 24C YET.' I SOON REALIZED THAT I HAD STOPPED PAST THE HOLD SHORT LINE FOR RWY 24L; BUT SHORT OF THE RWY. CLE TWR THEN CANCELED THE TKOF CLRNC FOR ANOTHER ACFT THAT HAD NOT YET TAKEN THE RWY AND CLRED US ACROSS RWY 24L TO PARKING. HOW DID THIS HAPPEN? I EXPECTED TO CLR RWY 24C BEFORE I WOULD HAVE TO HOLD SHORT OF RWY 24L. BUT THE CLOSE PROX OF THESE RWYS DOES NOT ALLOW THIS. YOU HAVE TO HOLD SHORT OF RWY 24L ON RWY 24C. THIS MAKES THE CLRNC 'CLRED ACROSS RWY 24C' SOMEWHAT MISLEADING -- NOT AN EXCUSE; JUST AN OBSERVATION. I WILL BET MY 401K THAT THIS RWY INCURSION WILL HAPPEN AGAIN. I CAN ONLY THINK OF ONE WAY YOU CAN PREVENT THIS FROM HAPPENING AGAIN. ATC SHOULD HOLD EVERYONE SHORT OF RWY 24C UNTIL THEY ARE CLRED TO CROSS RWY 24L. A LESS EFFECTIVE MEASURE WOULD BE TO CHANGE THE CLRNC TO 'HOLD SHORT OF RWY 24L ON RWY 24C.' THIS NEW CLRNC WOULD HIGHLIGHT THE POS OF THE UNUSUAL HOLD SHORT LINE. I HAVE JUST PROVEN THAT THE NOTE ON OUR ACFT CHART WILL NOT PREVENT THIS IN THE FUTURE. OBVIOUSLY; TWR HAS SEEN THIS BEFORE AND DID A GREAT JOB TODAY. HOWEVER; BAD WX; NIGHT OR A BUSY CTLR AND WE HAVE AN ENTIRELY DIFFERENT OUTCOME. I HAVE BEEN TO CLE MANY TIMES BEFORE AND CONSIDER MYSELF FAMILIAR WITH THE ARPT. I WAS THERE THE PREVIOUS DAY; IN FACT. SUPPLEMENTAL INFO FROM ACN 607230: I NOW REALIZE THE IMPORTANCE OF KEEPING MY HEAD UP AND OUTSIDE THE ACFT. AT THE TIME OF THIS INCURSION; I WAS ACCOMPLISHING THE AFTER LNDG CHKLIST.